The Ultimate Guide to Safe Withdrawal Rates – Part 18: Flexibility and the Mechanics of CAPE-Based Rules

Welcome back to the newest installment of the Safe Withdrawal Rate Series. To go back and start from the beginning, please check out Part 1 of the series with links to all the other parts as well.

Today’s post is a follow-up on some of the items we discussed in the ChooseFI podcast a few weeks ago. How do we react to a drop in the portfolio value early on during our retirement? Recall, it’s easy not to worry too much about market volatility when you are still saving for retirement. As I pointed out in the Sequence of Return Risk posts (SWR series Part 14 and Part 15), savers can benefit from a market drop early during the accumulation phase if the market bounces back eventually. Thanks to the Dollar Cost Averaging effect, you buy the most shares when prices are down and then reap the gains during the next bull market. That has helped the ERN family portfolio tremendously in the accumulation phase in 2001 and 2008/9.

But retirees should be more nervous about a market downturn. Remember, when it comes to Sequence of Return Risk, there is a zero-sum game between the saver and the retiree! A market drop early on helps the saver and thus has to hurt the retiree. What should the retiree do, then? The standard advice to early retirees (or any retiree for that matter) is to “be flexible!” Great advice! But flexible how? We are all flexible around here. I have yet to meet a single person who claims to be completely inflexible! “Being flexible” without specifics is utterly useless advice. It’s a qualitative answer to an inherently quantitative problem. If the portfolio is down by, say, 30% since the start of our retirement, then what? Cut the withdrawal by 30%? Keep withdrawals the same? Or something in between?

How flexible do I have to be to limit the risk of running out of money?

Fixed vs. Variable Withdrawal Rules

As we mentioned in the ChooseFI podcast and elsewhere: Nobody will ever set a fixed withdrawal amount and then just watch the portfolio dwindle away after years of poor returns. One way to prevent premature depletion is to set the withdrawals to one constant percentage of the portfolio every year (or month). The unpleasant side effect of this so-called Constant Percentage Rule: Withdrawals become just about as volatile as the portfolio. Let’s look at the hypothetical numerical example below (actual data will follow soon, be patient, everybody!). We start with a million dollar portfolio and an initial withdrawal of $40,000. We get returns of -30%,-10%,+20%,+20%, and +20% over the next 5 years, so the stock index actually recovers again (cumulative compound return of +9% after 5 years).

With a fixed withdrawal amount ($40k every year) we end up with only slightly more than $800,000. In contrast, withdrawing 4% of the portfolio value at the beginning of the year we are able to mitigate that sequence of return risk at least somewhat. We finish at $887k. But it’s at the cost of much lower withdrawals along the way. In fact, the withdrawals drop by slightly more than the market: -32.8% in the second year (from $40,000 to $26,880). That’s because the second year withdrawal is reduced by both the first year market drop and the previous year’s withdrawal. Bummer! And after a 10% market drop in year 2, the year 3 withdrawal falls by, you guessed it, slightly more than the market performance the previous year: -13.6%.

Numerical Example: Readjusting the withdrawals to 4% every year depletes the portfolio less but also means significant reductions in the withdrawals.

So, as we said in one of the Sequence of Return post (Part 15): dynamic withdrawals don’t really avoid sequence risk. True, you mitigate the impact of sequence risk on the final portfolio value, but it’s at the cost of lower withdrawals along the way. There is no free lunch and there’s no way to completely avoid sequence risk!

For how long do we have to be flexible?

So, we might endure a significant drop in withdrawals. Fine! Most people can deal with that, at least for a few years. Cut expenses, maybe get a side gig, move to a country with lower living expenses and/or defer some expenses such as replacing durable items. Surely, we can all be that flexible for a year or two, or maybe even five.

But can we be flexible for 28 years?

That’s how long it took to get back to the initial withdrawal amount for the January 1966 retirement cohort! See the chart below of the time series of withdrawals per $100 of initial capital for four different unfortunate retirement cohorts that were hit with an unhealthy dose of sequence of return risk:

The 1929 cohort that suffered through the Great Depression needed 26 years to recover the initial real purchasing power. With a 60% drop in between!

The 1966 cohort needed 28 years to recover from the perfect storm of lackluster returns in the late 60s, then four recessions (1970, 1973-75, 1980, 1982-82) with poor equity returns, especially in 1974 and 1982. For 11 years in a row, withdrawals were 40% or more below the initial!

The year 2000 cohort is still under water after 17 years despite the strong bull market over the past 8 years! That initial $40,000 withdrawal out of a million dollar portfolio dropped to about $20k at the bottom of the Global Financial Crisis and it’s now at just under $34,000!

The 2007 cohort actually recovered after “only” 7 years. So, there’s some good news! It appears that one single bear market is something we can handle with a constant percentage rule. Two bear markets in one decade? Not so much, that’s why the year 2000 cohort still hasn’t recovered!

Rolling 12-month withdrawals per $100 of initial capital under the 4% constant percentage rule (80% stocks, 20% bonds). This dynamic withdrawal rule avoids running out of money but could generate deep and extended multi-decade drawdowns in withdrawals! Notice that the 2000 retirement cohort still hasn’t recovered its initial withdrawal amount after over 17 years!

But don’t get me wrong! The 4% constant percentage rule did eventually return to its original portfolio value for the 1929, 1966 and 2007 cohorts (and thus the original withdrawal amount) and it will likely recover even for the year 2000 cohort, which is much better than the stubborn, fixed withdrawal amount (CPI-adjusted). Both the 1929 and 1966 cohorts would have depleted the portfolio within 30 years if they used the traditional 4% rule, i.e., 4% initial withdrawal followed by CPI-adjustments irrespective of portfolio performance.

Is there a “better” dynamic withdrawal rule?

Personally, I find the volatility of withdrawals and the depth and the duration of withdrawal drawdowns quite troubling. Again, I prefer to tighten the belt by 50% for a while or even a whole decade over ending up completely penniless. But there has to be a better way to deal with sequence of return risk, right?

One method to soften the impact is to tie the withdrawal amount (Wt) to not just the portfolio value (Pt) multiplied by a constant percentage (a) but also to an equity valuation metric, such as the Shiller CAPE, see the formula below. Of course, we would use the CAEY (Cyclically-adjusted Earnings Yield), which is the inverse of the CAPE. Notice that the constant percentage rule is simply a special case of the CAPE-rule if we set b=0 and a=4% (or whatever your desired constant percentage may be):

CAPE withdrawal formula. Notice that the constant percentage rule

Why the Shiller CAPE is uniquely suited for dealing with equity volatility

Let’s look at the mechanics of the CAPE formula in more detail. The problem with the constant percentage rule is that the withdrawal amount is proportional to the portfolio value. The portfolio went down by 30%? So does our withdrawal amount! The CAPE rule, on the other hand, has a way to cushion the drop. If the portfolio value takes a nosedive due to an equity market drop, then the CAPE will drop with it. That means the CAEY, which is the inverse of the CAPE, will then rise. It will not reverse the impact of the portfolio drop but certainly cushion the drop in withdrawals:

Under the constant percentage rule, the withdrawals will move in sync with the portfolio value. In contrast, tying the withdrawals to economic fundamentals has the potential to soften the fall in withdrawals in case of a bear market!

Why would the CAPE fall? The CAPE is the equity price index divided by a 10-year average earnings measure. 10-year rolling average earnings are moving very, very slowly, see the chart below; I plot the S&P500 price index (in 2017 dollars) and the 10-year rolling average earnings (also in 2017 dollars) that Prof. Shiller uses in his CAPE calculation. Notice something? The earnings line is much smoother, specifically, it hardly ever decreases even during recessions. That’s by construction; that’s where the name the name cyclically-adjusted comes from, remember? So when the stock market drops by x%, then, as a rule of thumb, the CAPE drops by roughly that much and thus the CAEY will increase. This will cushion the drop in withdrawals! In other words, by tying our withdrawals to earnings we’re bound to have a much smoother ride in withdrawals!

S&P500 Price Index and 10-year rolling earnings, CPI adjusted and on a log-scale (to make growth rates comparable across time).

Want to see how this cushioning effect works in practice? See the chart below. Whenever the portfolio has poor returns (blue line down) the CAPE-rule cushions the fall in withdrawals by raising the SWR. But it also works in the opposite direction. When the portfolio performs very well, then the SWR will move down again!

1Y portfolio return vs. the 1Y change in the CAPE-based Safe Withdrawal Rate. In response to a drop in the portfolio, the SWR increases! 80% equities, 20% bonds, SWR=1.75%+0.5*CAEY.

Just a side note: we can also expand the formula to include bond and cash yields in the CAPE-based formula because some portion of the portfolio is obviously invested in bonds or cash. I will show an example of that later:

Historical simulations of different CAPE rules

Let’s look how different parameterizations of this CAPE-based withdrawal formula would have performed over time. I take 8 different models:

CAPE 1.00/0.5: a=1% and b=0.5. This is the traditional CAPE-based rule that’s set as the default at cFIREsim. With the current CAPE at 30, this implies a pretty measly SWR of just under 2.7%!

CAPE 1.50/0.5: a=1.5% and b=0.5. Because the 1% intercept seemed a bit conservative, let’s raise the intercept by 0.5%.

CAPE 1.75/0.5: a=1.75% and b=0.5. Even slightly more aggressive than Rule 2!

CAPE 2.08/0.4: Let’s see what happens when we lower the CAEY multiplier to 0.4. But in exchange for that, I also increase the intercept to generate the same August 2017 withdrawal rate as rule 3.

CAPE 1.42/0.6: Now, let’s increase the multiplier and lower the intercept. Again we target the same current withdrawal rate as in rules 3 and 4.

“CAPE robust”: I use the Excel solver to maximize the August 2017 withdrawal rate subject to a constraint of never experiencing more than a 30% drawdown in withdrawals over in the post-1950 sample. I let the solver pick the parameters a,b,c, and d. Now I get a weight of 0.359 on the CAPE and +0.102 on the bond yield, but also a negative weight on the cash yield. Makes sense: The bond yield is something inherently nominal while we try to determine a real withdrawal rule. Taking the term-spread between 10-year bonds and cash seems more reasonable for the withdrawal rate rule.

“best of 3” is a weighted average of the rules 4, 6 and 8. The weights are calibrated to again reach the same August 2017 SWR as in rules 3, 4 and 5, i.e., 3.41%.

The constant percentage rule (4%), i.e., a=4% and all other parameters set to zero.

CAPE rule parameters

Some other assumptions:

In the portfolio we hold 80% stocks, 20% bonds, rebalanced monthly.

The withdrawals take place at the beginning of each month using the end of the previous month’s portfolio value, CAPE and bond/cash yield values.

The monthly withdrawal is 1/12 of the amount calculated. To smooth out some of the monthly fluctuations, I look at 12-month rolling withdrawal amounts. This would also make the exercise more comparable to other studies that use annual data only.

Simulation results

In the table below are some stats from my simulations of 12-month rolling withdrawal amounts. The stats I’m interested in:

Volatility of 12-month percentage changes in withdrawals

Annualized volatility of the portfolio

The worst 1-year drop in the withdrawal

The worst 20-year drop in the withdrawal

The worst 20-year drawdown in the withdrawal (which can clearly be worse than the 20-year-point-to-point drop, when the consumption trough occurs, say, after 12 years).

All the above stats are calculated for the entire sample and for the post-1950 period.

I also display the drawdown of withdrawals peak to bottom for the 4 prominent crises: the Great Depression, the 1970s (and early 80s), the dot-com bubble and the Global Financial Crisis.

These go back to some of the criteria I proposed in Part 11: how to grade dynamic withdrawal rules. Remember, dynamic rules don’t usually run out of money. So we need some other criteria to grade their performance and to compare different rules!

Results:

The constant 4% rule has consistently the worst volatility and drawdown stats. The withdrawals are roughly as volatile as the portfolio. The drawdowns from the initial withdrawal to the bottom are routinely 50% or more in some of the crises, even close to 60% in the 1970s. So, the retiree during the 1970s would have to be flexible enough to cut annual withdrawals from, say $40,000 to $16,000 per year. Of course, this rule also has the highest current withdrawal rate at 4%. That’s the tradeoff: the more generous the SWR the more flexibility will be required if there’s a bear market!

The CAPE-based rules have the same portfolio return volatility (by construction: all simulations are using an 80/20 portfolio). But their withdrawal volatility is significantly smaller than the portfolio volatility and more than 50% smaller than under the constant 4% rule. All of the other risk measures also look much better than under the constant percentage rule. But then again, the current withdrawal amounts implied by the CAPE are roughly 15% smaller. But considering that I have proposed 3.25% elsewhere, I was positively surprised that some of the dynamic rules now imply a withdrawal rate of 3.41% even with a CAPE at 30!

Quite intriguingly, the CAPE-rules handled the Great Depression extremely well. The CAPE was at 30+ in 1929 and then dropped to 5(!) in 1932. You would have withdrawn only 3% at the peak and over 10% p.a. at the bottom, so even after a precipitous drop, the withdrawal amount was not reduced that much. But that was OK because the market rebounded very rapidly in the mid-1930s.

More challenging than any other crisis in recent history: The 1970s! As mentioned above, between 1970 and 1982 we had four recessions, two of them major. What’s worse, due to the inflation shock and rising bond yields, bonds got hammered and negated any diversifying benefit in this episode! Under the constant percentage rule, a $40,000 initial withdrawal would have been decimated to $16,000 in the early 80s. Withdrawals would have been below $25,000 for 11 straight years, see the chart for the January 1966 retirement cohort, below. Even with the CAPE-based rules, retirees had to tighten the belt by 20 to 36%. It’s better than the roughly 60% drawdown under the constant percentage rule, but the CAPE-rules also took even longer to recover than 28 years!

Withdrawal amounts under different CAPE rules for the January 1966 retirement cohort. 80% equities, 20% bonds. Under the constant percentage rule, a $40,000 initial withdrawal would have been decimated to $16,000 in the early 80s. Withdrawals would have been below $25,000 for 11 straight years!

Other dynamic withdrawal rules:

Michael Kitces proposed adjusting the withdrawal rates according to the Shiller CAPE. The adjustments come in discrete steps: SWR=4.5% if CAPE>20, SWR=5.0% if CAPE between 12 and 20, SWR=5.5% if CAPE<12. I find this rule very unappealing. The jumps in the withdrawal rates are a) not big enough to effectively smooth out the withdrawal path and b) are completely discrete so most of the time there is no smoothing at all and we’re back to a simple constant percentage rule with all the unwanted volatility of withdrawals. I also find the 4.5% SWR for today’s CAPE regime quite high. It may be fine for a 65-year old retiree who is comfortable with capital depletion but certainly not for a 35-year old retiree with a potential 60-year horizon.

The Bogleheads VPW(Variable Percentage Withdrawals) is a variation of the constant percentage rule. It takes into account that the investment horizon shrinks as people age, thus, the VPW methodology calculates an increasing path of SWRs to account for that. If you’re fine with depleting your capital then that’s an appropriate thing to do. Personally, I’d prefer to preserve the capital for future generations and for charitable causes. But definitely, as a safety margin, one could switch to capital depletion in case of a major drawdown. For example, if after 10 years (or certainly 20 years) of a 60-year retirement horizon we like to increase our withdrawals we could simply switch from capital preservation to (at least partial) capital depletion and easily gain a bump of 20% or more in withdrawals. That will easily bring back the CAPE-based rules back to normal.

Guyton-Klinger: We wrote about this method in Part 9 and Part 10 of this series and also in the case study in Part 11. Qualitatively, this method displays some of the same problems as the constant percentage rule: steep and extended drawdowns in withdrawals. The more I look into this rule the more I dislike it. GK puts “guardrails” around the withdrawal percentages. But volatility in withdrawal percentages is not the problem. The volatility of withdrawal amounts is what bothers me! In fact, the CAPE-based rules work so well because of the dynamic withdrawal percentages and their ability to smooth out the market volatility!

Conclusion

Flexibility is a useful tool when dealing with the prospect of a drop in the portfolio value early on in our retirement (Sequence of Return Risk). But it’s also a double-edged sword. While eliminating the risk of completely running out of money after 30 years we increase the risk of steep cuts in withdrawals along the way. If your notion of flexibility is to “maybe forego the CPI adjustments for a few years” or “cut the cable bill for the duration of market drop” then that may be enough flexibility for very small market moves. But major recessions and bear markets require drastic multi-year, even decade-long reductions in withdrawals.

One hedge against this is to tie the withdrawal amounts to economic fundamentals, especially corporate earnings. These CAPE-based rules will withdraw a little bit less than 4% when equities are expensive (i.e., today!), but can also afford a slightly smoother ride through the various bear market scenarios considered here! It’s the natural extension of what we stressed in Part 17 of the series: The safe withdrawal rate has to respond to market conditions (in addition to idiosyncratic factors). But we can’t just set the initial SWR and then never touch it again. We should keep updating the subsequent withdrawal rates to reflect changing economic and financial conditions! A CAPE-based rule can do this and it’s intuitive, systematic and easy to implement!

We hope you enjoyed today’s post! Please leave your comments and suggestions below and also check out the other parts of the series!

108 thoughts on “The Ultimate Guide to Safe Withdrawal Rates – Part 18: Flexibility and the Mechanics of CAPE-Based Rules”

Thanks for the analysis. We have been intrigued by the CAPE rule, but have not been able to find research on setting the parameter values (a, b, c, and d). Question for you….in this analysis, your scenario #1 had a=1.0 and b=0.5. What were the c & d parameters since you assumed the portfolio was 80% stocks and 20% bonds (and the the c parameter pertains to bonds)? Please keep up the good work and a prosperous 2019!

Great question!
You know, I tried to play around with the c and d parameters and the results didn’t really change much. I’d like to keep it simple and ignore the bond valuation parameters. As long as you keep the equity portion high enough (70% or better 80%) the equity valuation parameters are all that matter.
Happy New Year!

In regards to the CAPE-based SWR, and SWR in general, can you please confirm the following in regards to tax treatment? As a simple math example, let’s say the CAPE is 30, and therefore the SWR is 3.17%. Let’s say your investable net worth is $10m, and your LTCG tax rate is 23.8%. Then that means your monthly withdrawal would be $26,389, and your monthly “budget” would be $20,108 after tax dollars, correct? Or in other words, your effective SWR after tax considerations would be a mere 2.41%. Does that make sense?

Last question, when using the CAPE-based SWR, there doesn’t appear to be any adjustment for CPI-inflation, correct? In other words, SWR is simply just a function of CAPE per the equation [i.e. SWR = 1.5% + 0.5*(1/CAPE)], regardless of inflationary changes over time. Whereas if you’re using a fixed method for safe withdrawal such as $300,000 on $10m in year 1, you’d increase your withdrawal to $306,000 in year 2 (assuming inflation of 2%), $312,120 in year 3, and so on..

Apologies in advance for the simple questions, double apologies if it’s been addressed elsewhere that I’m not seeing. I’m planning to retire within the next couple years (40 years old), and am just now wrapping my mind around this new stage of life.

Very important point: the withdrawals are pre-tax and for very large portfolios you get a high marginal tax and a large impact from taxes.
For a $2m portfolio you may be able to keep all of your income in the 0% bracket!
Also, you pay taxes only on the capital gains not when withdrawing the cost basis.

The CAPE-based SWR is not explicitly adjusted for inflation, but if you do this right then the portfolio will keep up with inflation and so will your withdrawal ammounts. But there have been instances where the withdrawal amounts fell for extended periods. Which is what all “flexibility rules” do (see parts 23-25). It’s then a matter of figureing out how much erosion of your (real) withdrawals can you stomach.

Thanks! Yes, I figured it would be a big mistake not to consider taxes. There isn’t much on the subject of taxes in the FIRE community in regards to SWR, as I suspect most fall within the leanFIRE and regular FIRE communities and thus have a 0% LTCG tax bracket, but the FatFIRE community is typically overlooked in this regard, I think it’s a good exercise for everyone to consider regardless of portfolio size, as capital gains tax rates could look quite a bit different for everyone 30, 40, 50+ years from now, as the rates varied greatly in years past.

KOW….I won’t reply on the tax question as that is out of my realm. However, on the CPI question I will offer my perspective. The CAPE number inherently reflects the equity market and that same market will have inflationary responses. Therefore, I don’t plan on doing any CPI adjustment when I use the CAPE equation. Keep in mind that the CAPE equation will cause volatility in the annual withdrawal amount. If the volatility is too much, then the “b” parameter can be decreased which lowers the impact form CAPE for that year. Big ERN has done studies on various “a” and “b” parameters in Part 11 of his fantastic series, so it may be worth a read.

This simulation is not for a particular time-frame. I did one long run of 145 years and checked what the worst 1y drop and 20y drop and 20y drawdown were along this entire long history.
The 80/20 portfolio simulated here was using only the CAPE. Not the bond yield and not the cash yield either.

Absolutely love this analysis; I’ve been back to this post multiple times over the last few months, and I keep wondering the same thing: why not just use the CAEY as the withdrawal rate? I guess you could have really high withdrawals in a downturn, but at least as it relates to the concern around over-withdrawing during times of high valuation, it seems like an heuristic of “spending the earnings” (not just the dividend) should provide pretty good guidance if you want to avoid capital depletion. I look at my real estate portfolio the same way; I don’t pay attention to the valuation of the property, I only (conservatively) model the earnings that my equity in the property generates after expenses…

Thanks!
You can simulate how that looks like. In the Google Sheet (Part 28) there’s a feature.
Sett ing a=0 and b=1, you’ll get nasty, permanent declines in purchasing power. Worst is where the withdrawal amount is 72% below the initial amount. It’s not as bad as the 4% Rule (worst case =-100%) but almost as bad.
The 0.5 factor before the CAEY is the sweet spot:
at 0.0 (and b=4%) you’d have too much short-term vol
at 1.0 you’d have too much risk of long-term depletion.
At 0.5 you balance those two risks.

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